The first observation of the B0s→¯D*0ϕ decay is reported, with a significance of more than seven standard deviations, from an analysis of pp collision data corresponding to an integrated luminosity of 3 fb−1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction is measured relative to that of the topologically similar decay B0→¯D0π+π− and is found to be B(B0s→¯D*0ϕ)=(3.7±0.5±0.3±0.2)×10−5, where the first uncertainty is statistical, the second systematic, and the third from the branching fraction of the B0→¯D0π+π− decay. The fraction of longitudinal polarization in this decay is measured to be fL=(73±15±4)%. The most precise determination of the branching fraction for the B0s→¯D0ϕ decay is also obtained, B(B0s→¯D0ϕ)=(3.0±0.3±0.2±0.2)×10−5. An upper limit, B(B0→¯D0ϕ)<2.0 (2.3)×10−6 at 90% (95%) confidence level is set. A constraint on the ω−ϕ mixing angle δ is set at |δ|<5.2° (5.5°) at 90% (95%) confidence level.